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NECO SSCE Mathematics study materials
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NECO SSCE Mathematics practice questions

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Question 1Number and Numeration

Convert 1101₂ to a number in base ten.

  1. 14
  2. 12
  3. 11
  4. 13 Correct answer.

Explanation

In base two, each digit is a power of two from right to left. So 1101₂ = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13.

Question 2Number and Numeration

Express 0.000045 in standard form.

  1. 4.5 × 10⁵
  2. 4.5 × 10⁻⁵ Correct answer.
  3. 45 × 10⁻⁶
  4. 4.5 × 10⁻⁴

Explanation

Standard form is A × 10ⁿ with 1 ≤ A < 10. Moving the decimal point five places to the right in 0.000045 gives 4.5, so the exponent is −5.

Question 3Number and Numeration

Find the lowest common multiple of 12 and 18.

  1. 24
  2. 36 Correct answer.
  3. 72
  4. 6

Explanation

Write 12 = 2² × 3 and 18 = 2 × 3². The LCM takes the highest power of each prime: 2² × 3² = 4 × 9 = 36.

Question 4Number and Numeration

Simplify 4/(√7 − √3) by rationalising the denominator.

  1. 2(√7 + √3)
  2. √7 − √3
  3. √7 + √3 Correct answer.
  4. (√7 + √3)/2

Explanation

Multiply numerator and denominator by the conjugate √7 + √3. The denominator becomes (√7)² − (√3)² = 7 − 3 = 4, so 4(√7 + √3)/4 = √7 + √3.

Question 5Number and Numeration

Evaluate 121₃ + 22₃, giving your answer in base three.

  1. 201₃
  2. 1012₃
  3. 220₃ Correct answer.
  4. 210₃

Explanation

Convert to base ten: 121₃ = 1×9 + 2×3 + 1 = 16 and 22₃ = 2×3 + 2 = 8. Their sum is 24, and 24 = 2×9 + 2×3 + 0 = 220₃.

Question 6Number and Numeration

If 3^(2x−1) = 27, find the value of x.

  1. 4
  2. 3
  3. 1
  4. 2 Correct answer.

Explanation

Write 27 as 3³, so 3^(2x−1) = 3³. Equating exponents gives 2x − 1 = 3, hence 2x = 4 and x = 2.

Question 7Number and Numeration

In a class of 40 students, 25 study Mathematics, 20 study Physics, and 10 study both subjects. How many students study neither Mathematics nor Physics?

  1. 5 Correct answer.
  2. 15
  3. 0
  4. 10

Explanation

The number studying at least one subject is n(M ∪ P) = 25 + 20 − 10 = 35. Therefore the number studying neither is 40 − 35 = 5.

Question 8Number and Numeration

A trader bought an article for ₦2,500 and sold it for ₦3,000. What is the percentage profit?

  1. 15%
  2. 30%
  3. 20% Correct answer.
  4. 25%

Explanation

Profit = ₦3,000 − ₦2,500 = ₦500. Percentage profit is (500/2500) × 100% = 20%.

Question 9Number and Numeration

Given that log 2 = 0.3010 and log 3 = 0.4771, find log 1.5.

  1. 0.7781
  2. 0.1761 Correct answer.
  3. 0.3010
  4. 0.1505

Explanation

Use log(3/2) = log 3 − log 2. Substituting the given values gives 0.4771 − 0.3010 = 0.1761.

Question 10Number and Numeration

The ratio of boys to girls in a school is 5:4. When 20 more boys join the school, the ratio becomes 3:2. How many girls are in the school?

  1. 60
  2. 80 Correct answer.
  3. 120
  4. 100

Explanation

Let boys = 5k and girls = 4k. After 20 boys join, (5k + 20)/(4k) = 3/2. Cross-multiplying gives 10k + 40 = 12k, so k = 20 and girls = 4k = 80.

Question 11Number and Numeration

Express 45 in base ten as a number in base two.

  1. 110101₂
  2. 101101₂ Correct answer.
  3. 101011₂
  4. 110011₂

Explanation

45 = 32 + 8 + 4 + 1 = 2⁵ + 2³ + 2² + 2⁰. Placing 1 in the 2⁵, 2³, 2² and 2⁰ places and 0 in the 2⁴ and 2¹ places gives 101101₂.

Question 12Number and Numeration

Express 3 460 000 in standard form.

  1. 3.46 × 10⁵
  2. 3.46 × 10⁶ Correct answer.
  3. 3.46 × 10⁷
  4. 34.6 × 10⁴

Explanation

Standard form is written as A × 10ⁿ, where 1 ≤ A < 10. Moving the decimal point six places to the left in 3 460 000 gives A = 3.46, so the number is 3.46 × 10⁶.

Question 13Number and Numeration

Approximate 4 837 to two significant figures.

  1. 5 000
  2. 4 900
  3. 4 840
  4. 4 800 Correct answer.

Explanation

The first two significant figures of 4 837 are 4 and 8. The next digit is 3, which is less than 5, so the 8 is not rounded up and all following digits become zeros, giving 4 800.

Question 14Number and Numeration

Simplify √50 + √18.

  1. 8√2 Correct answer.
  2. 4√2
  3. 2√17
  4. 8√4

Explanation

√50 = √(25 × 2) = 5√2 and √18 = √(9 × 2) = 3√2. Since the surds are now alike, 5√2 + 3√2 = 8√2.

Question 15Number and Numeration

In a survey, 20 students study Biology, 15 study Chemistry, 12 study Physics, 5 study Biology and Chemistry, 4 study Biology and Physics, 3 study Chemistry and Physics, and 2 study all three subjects. How many students study at least one of the three subjects?

  1. 33
  2. 47
  3. 35
  4. 37 Correct answer.

Explanation

Apply n(A ∪ B ∪ C) = sum of the single sets − sum of the pairs + the triple intersection. That gives (20 + 15 + 12) − (5 + 4 + 3) + 2 = 47 − 12 + 2 = 37.

Question 16Number and Numeration

Solve the equation log₃(x + 2) = 2.

  1. 1
  2. 11
  3. 7 Correct answer.
  4. 9

Explanation

Writing the logarithmic statement in index form gives x + 2 = 3² = 9. Subtracting 2 from both sides gives x = 7.

Question 17Number and Numeration

y varies directly as the square of x, and y = 48 when x = 4. Find y when x = 5.

  1. 192
  2. 75 Correct answer.
  3. 60
  4. 45

Explanation

Direct variation with the square of x means y = kx². Substituting gives 48 = k(4²) = 16k, so k = 3; therefore when x = 5, y = 3(5²) = 75.

Question 18Number and Numeration

Find the next term of the sequence 3, 8, 15, 24, …

  1. 36
  2. 35 Correct answer.
  3. 48
  4. 33

Explanation

The differences between successive terms are 5, 7 and 9, increasing by 2 each time. The next difference must be 11, so the next term is 24 + 11 = 35.

Question 19Number and Numeration

Solve for x in the equation 9ˣ = 27⁽ˣ ⁻ ²⁾.

  1. 6 Correct answer.
  2. 3
  3. −6
  4. 2

Explanation

Express both sides in base 3: 9ˣ = 3²ˣ and 27⁽ˣ ⁻ ²⁾ = 3³ˣ ⁻ ⁶. Equating the exponents gives 2x = 3x − 6, so x = 6, which checks since both sides then equal 3¹².

Question 20Number and Numeration

Express the recurring decimal 0.454545… as a common fraction in its lowest terms.

  1. 11/25
  2. 5/11 Correct answer.
  3. 9/20
  4. 4/9

Explanation

Let x = 0.454545…, then 100x = 45.4545… Subtracting the first equation from the second gives 99x = 45, so x = 45/99 = 5/11.

Question 21Number and Numeration

Convert 342₅ to a number in base ten.

  1. 117
  2. 87
  3. 107
  4. 97 Correct answer.

Explanation

In base five the place values are powers of 5: 25, 5 and 1. Therefore 342₅ = 3×25 + 4×5 + 2×1 = 75 + 20 + 2 = 97.

Question 22Number and Numeration

Express 0.00058 in standard form.

  1. 5.8 × 10⁻³
  2. 5.8 × 10⁻⁴ Correct answer.
  3. 5.8 × 10⁻⁵
  4. 5.8 × 10⁻⁶

Explanation

Standard form is A × 10ⁿ where 1 ≤ A < 10. Moving the decimal point in 0.00058 four places to the right gives 5.8, so the index is −4.

Question 23Number and Numeration

Approximate 0.004567 to two significant figures.

  1. 0.00457
  2. 0.0046 Correct answer.
  3. 0.0050
  4. 0.0045

Explanation

The first two significant figures of 0.004567 are 4 and 5; the next digit is 6, so the 5 is rounded up to 6. Hence the value is 0.0046 to two significant figures.

Question 24Number and Numeration

Find the highest common factor of 84 and 126.

  1. 21
  2. 42 Correct answer.
  3. 84
  4. 14

Explanation

Write 84 = 2² × 3 × 7 and 126 = 2 × 3² × 7. The HCF takes the lowest power of each common prime factor: 2 × 3 × 7 = 42.

Question 25Number and Numeration

A sum of ₦84,000 is shared among three people in the ratio 2:3:5. How much does the person with the largest share receive?

  1. ₦42,000 Correct answer.
  2. ₦16,800
  3. ₦25,200
  4. ₦50,400

Explanation

The ratio has 2 + 3 + 5 = 10 equal parts. The largest share is 5 parts, so it is (5/10) × ₦84,000 = ₦42,000.

Question 26Number and Numeration

In a survey of 50 people, 30 read newspaper A, 25 read newspaper B, and 10 read both. How many read neither newspaper?

  1. 15
  2. 5 Correct answer.
  3. 10
  4. 20

Explanation

The number who read at least one newspaper is 30 + 25 − 10 = 45. Since 50 people were surveyed, the number who read neither is 50 − 45 = 5.

Question 27Number and Numeration

If log₄ x = 3, find the value of x.

  1. 12
  2. 81
  3. 64 Correct answer.
  4. 16

Explanation

By the definition of logarithm, log₄ x = 3 means 4³ = x. Since 4³ = 64, x = 64.

Question 28Number and Numeration

y varies inversely as x, and y = 8 when x = 3. Find y when x = 6.

  1. 16
  2. 2
  3. 4 Correct answer.
  4. 8

Explanation

For inverse variation y = k/x. Substituting y = 8 and x = 3 gives k = 24, so y = 24/6 = 4 when x = 6.

Question 29Number and Numeration

Express the recurring decimal 0.161616… as a common fraction in its lowest terms.

  1. 16/99 Correct answer.
  2. 1/6
  3. 8/45
  4. 4/25

Explanation

Let x = 0.161616… . Then 100x = 16.161616… . Subtracting gives 99x = 16, so x = 16/99.

Question 30Number and Numeration

Solve for x in the equation 101ₓ = 26₁₀.

  1. 3
  2. 6
  3. 5 Correct answer.
  4. 4

Explanation

101ₓ means 1·x² + 0·x + 1 = x² + 1. Setting x² + 1 = 26 gives x² = 25, so x = 5 because a base must be greater than 1.

Question 31Number and Numeration

Convert 156 in base ten to a number in base eight.

  1. 224₈
  2. 324₈
  3. 234₈ Correct answer.
  4. 243₈

Explanation

Repeated division by 8 gives 156 ÷ 8 = 19 remainder 4, 19 ÷ 8 = 2 remainder 3, and 2 ÷ 8 = 0 remainder 2. Reading the remainders upwards gives 234₈.

Question 32Number and Numeration

Express 0.0000708 in standard form.

  1. 7.08 × 10⁻³
  2. 7.08 × 10⁻⁴
  3. 7.08 × 10⁻⁶
  4. 7.08 × 10⁻⁵ Correct answer.

Explanation

Standard form is A × 10ⁿ where 1 ≤ A < 10. Moving the decimal point five places to the right gives 7.08, so the power of ten is −5.

Question 33Number and Numeration

Find the lowest common multiple (LCM) of 12 and 18.

  1. 72
  2. 216
  3. 36 Correct answer.
  4. 6

Explanation

Write each number as a product of prime factors: 12 = 2² × 3 and 18 = 2 × 3². The LCM takes the highest power of each prime, so 2² × 3² = 36.

Question 34Number and Numeration

In a group of 30 students, 18 study French, 12 study Spanish, and 5 study both languages. How many students study only one of the two languages?

  1. 15
  2. 20 Correct answer.
  3. 10
  4. 25

Explanation

Subtract the 5 who study both from each subject total: 18 − 5 = 13 study only French and 12 − 5 = 7 study only Spanish. Adding these gives 13 + 7 = 20 students who study exactly one language.

Question 35Number and Numeration

Solve for x: log₂(x − 3) = 4.

  1. 19 Correct answer.
  2. 13
  3. 16
  4. 11

Explanation

Rewrite the logarithmic equation in exponential form: x − 3 = 2⁴ = 16. Adding 3 to both sides gives x = 19, and this value is valid because x − 3 > 0.

Question 36Number and Numeration

z varies jointly as x and y. If z = 24 when x = 3 and y = 4, find z when x = 5 and y = 2.

  1. 40
  2. 20 Correct answer.
  3. 10
  4. 30

Explanation

Joint variation means z = kxy. Substituting gives 24 = k(3)(4) = 12k, so k = 2. Then z = 2(5)(2) = 20.

Question 37Number and Numeration

Find the 10th term of the arithmetic sequence 5, 9, 13, ...

  1. 49
  2. 45
  3. 37
  4. 41 Correct answer.

Explanation

The first term is a = 5 and the common difference is d = 9 − 5 = 4. The nth term is a + (n − 1)d, so the 10th term is 5 + 9×4 = 41.

Question 38Number and Numeration

Simplify (27^(2/3)) ÷ (9^(1/2)).

  1. 1/3
  2. 3 Correct answer.
  3. 9
  4. 27

Explanation

27^(2/3) = (∛27)² = 3² = 9, and 9^(1/2) = √9 = 3. Therefore the expression equals 9 ÷ 3 = 3.

Question 39Number and Numeration

Express the recurring decimal 0.123123123... as a common fraction in its lowest terms.

  1. 41/333 Correct answer.
  2. 41/33
  3. 41/300
  4. 123/1000

Explanation

Let x = 0.123123...; then 1000x = 123.123123..., so 999x = 123. Thus x = 123/999 = 41/333 after dividing numerator and denominator by 3.

Question 40Number and Numeration

Rationalise the denominator of 6/(3 − √3).

  1. 2 + √3
  2. 3 + √3 Correct answer.
  3. 2 − √3
  4. 3 − √3

Explanation

Multiply numerator and denominator by the conjugate 3 + √3. The denominator becomes 3² − (√3)² = 9 − 3 = 6, so the expression simplifies to 6(3 + √3)/6 = 3 + √3.

Question 41Number and Numeration

How many significant figures are in the number 0.06070?

  1. 5
  2. 2
  3. 4 Correct answer.
  4. 3

Explanation

Leading zeros are not significant, but the zero between 6 and 7 is significant, and the final zero after 7 in the decimal part is also significant. Therefore the significant digits are 6, 0, 7 and 0, giving four significant figures.

Question 42Number and Numeration

Solve for x: 2^(x + 1) = 1/8.

  1. 2
  2. -2
  3. -4 Correct answer.
  4. 4

Explanation

Write 1/8 as 2^(-3). Since the bases are equal, equate the exponents: x + 1 = -3, so x = -4.

Question 43Number and Numeration

Which of the following fractions is the largest?

  1. 2/3 Correct answer.
  2. 3/5
  3. 5/8
  4. 7/12

Explanation

Using a common denominator of 120 gives 72/120, 75/120, 70/120 and 80/120 respectively. The largest numerator is 80, so 2/3 is the largest fraction.

Question 44Number and Numeration

Evaluate 1101₂ + 1011₂, leaving your answer in base two.

  1. 11000₂ Correct answer.
  2. 10100₂
  3. 10010₂
  4. 11010₂

Explanation

In base ten, 1101₂ = 13 and 1011₂ = 11, so the sum is 24. Converting 24 to base two gives 11000₂.

Question 45Number and Numeration

(3.2 × 10^4) × (2.5 × 10^(-2)). Express the result in standard form.

  1. 8 × 10^2 Correct answer.
  2. 8 × 10^6
  3. 8 × 10^3
  4. 8 × 10^(-8)

Explanation

Multiply the coefficients: 3.2 × 2.5 = 8.0. Add the powers of ten: 4 + (-2) = 2. Hence the product is 8 × 10^2, which is already in standard form.

Question 46Number and Numeration

The HCF of two numbers is 6 and their LCM is 72. If one number is 24, find the other.

  1. 18 Correct answer.
  2. 48
  3. 12
  4. 36

Explanation

For two positive integers, the product of the numbers equals HCF × LCM. Thus the other number is (6 × 72) ÷ 24 = 432 ÷ 24 = 18.

Question 47Number and Numeration

Simplify log₁₀6 + log₁₀15 − log₁₀9.

  1. 2
  2. 1 Correct answer.
  3. 3
  4. 0

Explanation

Use the laws log a + log b = log(ab) and log a − log b = log(a/b). The expression becomes log₁₀(6 × 15 ÷ 9) = log₁₀10. Since log₁₀10 = 1, the value is 1.

Question 48Number and Numeration

Simplify √50 + √18 − √8.

  1. 6√2 Correct answer.
  2. 4√2
  3. 8√2
  4. 10√2

Explanation

Simplify each term: √50 = 5√2, √18 = 3√2 and √8 = 2√2. Combining like surds gives 5√2 + 3√2 − 2√2 = 6√2.

Question 49Number and Numeration

Find the sum of the first 8 terms of the geometric progression 3, 6, 12, ...

  1. 384
  2. 510
  3. 765 Correct answer.
  4. 1530

Explanation

The first term is a = 3 and the common ratio is r = 2. The sum of the first 8 terms is S8 = a(r^8 − 1)/(r − 1) = 3(256 − 1)/1 = 765.

Question 50Number and Numeration

y varies partly as x and partly as x². When x = 1, y = 5; when x = 2, y = 14. Find y when x = 3.

  1. 36
  2. 27 Correct answer.
  3. 33
  4. 30

Explanation

Write y = ax + bx². Substituting the two pairs gives a + b = 5 and 2a + 4b = 14. Solving gives b = 2 and a = 3, so y = 3x + 2x². When x = 3, y = 9 + 18 = 27.